

from __future__ import annotations







def       lowercase					(	__A :					list[list[int]]		)				->			bool:





    '''simple docstring'''




    snake_case							:		Dict        =		len(__A		)
    # We need to create solution object to save path.
    snake_case							:		Union[str, Any]        =		[[0 for _ in range(__A		)] for _ in range(__A		)]
    snake_case							:		str        =		run_maze(__A ,    0 ,    0 ,    __A		)
    if solved:
        print("""\n""".join(str(__A		) for row in solutions		)		)
    else:
        print("""No solution exists!"""		)
    return solved







def       lowercase					(	__A :					list[list[int]] ,    __A :					int ,    __A :					int ,    __A :					list[list[int]]		)				->			bool:





    '''simple docstring'''




    snake_case							:		Any        =		len(__A		)
    # Final check point.
    if i == j == (size - 1):
        snake_case							:		str        =		1
        return True

    snake_case							:		str        =		(not i < 0) and (not j < 0)  # Check lower bounds
    snake_case							:		Union[str, Any]        =		(i < size) and (j < size)  # Check upper bounds

    if lower_flag and upper_flag:
        # check for already visited and block points.
        snake_case							:		Optional[int]        =		(not solutions[i][j]) and (not maze[i][j])
        if block_flag:
            # check visited
            snake_case							:		List[str]        =		1

            # check for directions
            if (
                run_maze(__A ,    i + 1 ,    __A ,    __A		)
                or run_maze(__A ,    __A ,    j + 1 ,    __A		)
                or run_maze(__A ,    i - 1 ,    __A ,    __A		)
                or run_maze(__A ,    __A ,    j - 1 ,    __A		)
            ):
                return True

            snake_case							:		Optional[int]        =		0
            return False
    return False


if __name__ == "__main__":
     import doctest

     doctest.testmod()







'''simple docstring'''


import math







def      snake_case_  (    SCREAMING_SNAKE_CASE__	):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE					:			Tuple							= math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

				return exponent == int(SCREAMING_SNAKE_CASE__	)







def      snake_case_  (    SCREAMING_SNAKE_CASE__ = 1 / 1_2345	):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE					:			str							= 0
				_SCREAMING_SNAKE_CASE					:			str							= 0

				_SCREAMING_SNAKE_CASE					:			int							= 3
				while True:
								_SCREAMING_SNAKE_CASE					:			Optional[int]							= (integer**2 - 1) / 4
								# if candidate is an integer, then there is a partition for k
								if partition_candidate == int(SCREAMING_SNAKE_CASE__	):
												_SCREAMING_SNAKE_CASE					:			int							= int(SCREAMING_SNAKE_CASE__	)
												total_partitions += 1
												if check_partition_perfect(SCREAMING_SNAKE_CASE__	):
																perfect_partitions += 1
								if perfect_partitions > 0:
												if perfect_partitions / total_partitions < max_proportion:
																return int(SCREAMING_SNAKE_CASE__	)
								integer += 1


if __name__ == "__main__":
				print(F"{solution() = }")




